Introduction to Gauge Theories (continued): Principal Bundles

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Scientia Egregia

Published on Streamed live on Sep 26, 2020
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Continuation of the video • Introduction to gauge theories: ... ------------------------------------------------------------------- My name is Antoine Bourget, I am a theoretical physicist, and I try to convey in video what I find elegant in mathematics and physics. To follow the news of the channel, and contact me, you can join the Discord server or follow me on social networks. If you want to donate, I also have a Tipeee Discord account: / discord Twitter: / antoinebrgt My personal website: http://www.antoinebourget.org Tipeee: https://fr.tipeee.com/scientia-egregia/ ------------------------------------------------------------------- Outline Part 1: Intuition and examples 00:00 Intuitive notion of bundle and examples 12:14 Examples of principal bundles with finite group (Möbius strip) 22:20 Examples of principal bundles with continuous groups 27:45 Principal bundle on spacetime Part 2: Technical definition 38:40 Principal bundle 1:00:10 Global section 1:05:20 Connection Part 3: Gauge invariance from the point of view of the bundle 1:13:54 Form of local connection from a local section 1:18:10 Gauge transformation 1:34:30 What happens passes with other groups 1:39:40 Opening on the topology of fibers, magnetic monopoles Conclusion 1:45:35 General summary 1:49:02 Questions To follow the news of the channel, you can join the Discord server or follow me on Twitter: Discord: / discord Twitter: / antoinebrgt My personal site: http://www.antoinebourget.org References: Bjorn Felsager, Geometry, Particles and Fields Theodore Frankel, The geometry of physics Mikio Nakahara, Geometry, Topology and Physics M. Daniel and CM Viallet, The geometrical setting of gauge theories of the Yang-Mills type (accessible at http://www.lpthe.jussieu.fr/~viallet/...)

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